Subcontests
(3)Combinatoric number theory
Find all integers n greater than or equal to 4 that satisfy the following conditions:[*] Take an arbitrary convex n-gon P on the coordinate plane whose vertices are lattice points (points whose coordinates are both integers). There are a total of n triangles that share two sides with P. Let S1,S2,…,Sn be their areas, and let S be the area of P. Then, the greatest common divisor of 2S1,2S2,…,2Sn divides the integer 2S.